Floquet topological superconductors with many Majorana edge modes: topological invariants, entanglement spectrum and bulk-edge correspondence

Abstract

One-dimensional Floquet topological superconductors possess two types of degenerate Majorana edge modes at zero and π quasienergies, leaving more room for the design of boundary time crystals and quantum computing schemes than their static counterparts. In this work, we discover Floquet superconducting phases with large topological invariants and arbitrarily many Majorana edge modes in periodically driven Kitaev chains. Topological winding numbers defined for the Floquet operator and Floquet entanglement Hamiltonian are found to generate consistent predictions about the phase diagram, bulk-edge correspondence and numbers of zero and π Majorana edge modes of the system under different driving protocols. The bipartite entanglement entropy further shows non-analytic behaviors around the topological transition point between different Floquet superconducting phases. These general features are demonstrated by investigating the Kitaev chain with periodically kicked pairing or hopping amplitudes. Our discovery reveals the rich topological phases and many Majorana edge modes that could be brought about by periodic driving fields in one-dimensional superconducting systems. It further introduces a unified description for a class of Floquet topological superconductors from their quasienergy bands and entanglement properties.

Anomalies-Rich Floquet superconductivities induced by joint modulation of dynamic driving and static parameters

“…Floquet systems could also be subjected to diverse potentials, such as tilted linear potential [39]and diagonal on-site potential in square lattice [40]. Floquet driving can be constructed upon different dimensional systems as well, such as one-dimensional (1D) and two-dimensional (2D) TSCs [41][42][43][44][45], forming higher-order topological phases with Majorana corner modes at 0 and π quasi-energies. For recent theoretical reviews, see [46][47][48].…”

Non-Hermitian Floquet Topological Matter—A Review

“…These spectral windings result in unique states of matter in periodically driven systems, such as Floquet semi-metals with Floquet band holonomy [65][66][67], degenerated edge modes at E = ±π (anomalous Floquet π modes) [68][69][70][71] and anomalous chiral edge states in Floquet topological insulators (FTIs) [72][73][74], which have no counterparts in static systems. Third, the driving field could assist in the formation of long-range, and even spatially non-decaying coupling among different degrees of freedom in a lattice [24], leading to Floquet phases with large topological invariants, rich topological transitions, and a substantial number of topological edge states [75][76][77][78][79][80][81][82]. These phases and boundary states go beyond the description of any static tight-binding models in typical situations (i.e., with finite-range or spatially decaying hopping amplitudes).…”